Estimating Volatility from Historical Data (page 295-298

Estimating Volatility from Historical Data (page 295-298 -...

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Estimating Volatility from Historical Data (page 295-298) 1. Take observations S 0 , S 1 , . . . , Sn on the variable at end of each trading day 2. Define the continuously compounded daily return as: 3. Calculate the standard deviation, s , of the ui ´s 4. The historical volatility per year estimate is: 1 u S S i i i = - ln 1 252 × s
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Estimating Volatility from Historical Data continued More generally, if observations are every τ years ( τ might equal 1/252, 1/52 or 1/12), then the historical volatility per year estimate is 2 τ s
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The Concepts Underlying Black- Scholes The option price and the stock price depend on the same underlying source of uncertainty. We can form a portfolio consisting of the stock and the option which eliminates this source of uncertainty. The portfolio is instantaneously riskless and must instantaneously earn the risk-free rate.
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Unformatted text preview: 3 The Black-Scholes Formulas (See page 299-300) 4 T d T T r K S d T T r K S d d N S d N e K p d N e K d N S c rT rT σ-= σ σ-+ = σ σ + + =---=-=--1 2 1 1 2 2 1 ) 2 / 2 ( ) / ln( ) 2 / 2 ( ) / ln( ) ( ) ( ) ( ) ( where The N ( x ) Function • N ( x ) is the probability that a normally distributed variable with a mean of zero and a standard deviation of 1 is less than x • See tables at the end of the book 5 Properties of Black-Scholes Formula • As S becomes very large c tends to S – Ke-rT and p tends to zero • As S becomes very small c tends to zero and p tends to Ke-rT – S • Notice that the formula includes 5 of 6 fundamental determinants of option value. – S, K, r, T, σ • Missing dividends 6...
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This note was uploaded on 01/19/2012 for the course FIN 4520 taught by Professor Lucyackert during the Spring '12 term at Kennesaw.

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Estimating Volatility from Historical Data (page 295-298 -...

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